Answer:
We conclude that:
[tex]b=a-cd;\quad \:c\ne \:0[/tex]
Hence, option A is true.
Step-by-step explanation:
Given the expression
[tex]\frac{a-b}{c}=d[/tex]
Solving for b
[tex]\frac{a-b}{c}=d[/tex]
Multiply both sides by c
[tex]\frac{\left(a-b\right)c}{c}=dc;\quad \:c\ne \:0[/tex]
simplify
[tex]a-b=dc;\quad \:c\ne \:0[/tex]
Subtract a from both sides
[tex]a-b-a=dc-a;\quad \:c\ne \:0[/tex]
Simplify
[tex]-b=dc-a;\quad \:c\ne \:0[/tex]
Divide both sides by -1; c≠0
[tex]\frac{-b}{-1}=\frac{dc}{-1}-\frac{a}{-1};\quad \:c\ne \:0[/tex]
simplify
[tex]b=a-cd;\quad \:c\ne \:0[/tex]
Therefore, we conclude that:
[tex]b=a-cd;\quad \:c\ne \:0[/tex]
Hence, option A is true.
